That does seem to make sense though. Imagine a bell and a flat wooden panel. The first has a high resonance frequency whereas the second one has a low one. And put them both in a room where speakers are playing and which one resonates the most and audibly? Not the bell but the panel.
I would guess that was at least part of the cause. The important point is that pushing resonance up in frequency will not improve their audibility unless resonant level falls as frequency rises. Harwood (and others) show that that is not the case.
David S
David S, thanks for the BBC paper. Shows that a thick-walled cabinet is not necessarily good. Also explains why I could never get a 60mm, 75kg thick-walled MDF speaker enclosure to sound right. Plagued with resonances even with bitumen and polyfill.
I dont think planet10 was claiming that resonant level falls but that it is harder to excite. And from the example i cited earlier it seems to make sense intuitively. Why is it that a panel of wood, with its low resonant frequency is easy to excite compared with a bell?
the Linkwitz table is interesting. He is outlining the case of a sealed box driver and a OB driver. Both are presumed to put out a constant 90 dB. That means the OB case needs a constant 6dB per EQ. The sealed box case will have constant acceleration and also constant force. The energy falls with frequency because constant acceleration equals falling velocity. Now this is the kinetic energy of the moving cone and not the energy or power being radiated. That is because the air load, which rises at 12dB per Octave for the driver to radiate flat power lets us have constant acceleration and falling velocity or falling kinetic energy.
The same applies to the surrounding cabinet. Linkwitz describes a pair of drivers and cabinet with 100 times the mass of the cones, so the cabinet moves 1/100th of the cone excursion. As frequency goes up the cone excursion will drop but so will the cabinet vibration. No matter, falling excursion can still have constant acceleration that would mean flat output for the driver and, equally, flat output from the reacting cabinet.
Linkwitz speculates that the falling energy would drive cabinet resonances less but overlooks that the reaction acceleration is constant. This explains why we do not see a constant 12dB per Octave fall in panel resonant activity in anyones actual measurements.
David S
I think he is claiming that, but unfortunately it is a nonsensical statement.
David
could you please explain why constant acceleration equals falling velocity and what velocity are you referring to? I'm trying to follow your argument and I dont fully follow it. The first mystery for me is why does the cone excursion decrease with frequency?
We are only interested in the sealed box. He has a direct entry for the energy imparted by the driver on the box. This represents at a minimum 2/3rds of the total energy put into the box that is available to excite a resonance.
None of the rest matters.
But you have to pump enuff energy (at the frequency of the resonance) to excite that resonance 1st.
I am claiming that at higher frequency there is less energy to excite the resonance. Just what Linkwitz says.
dave
This is the standard physics of the direct radiator loudspeaker. We can look at excursion, velocity, or acceleration. Velocity is the deriviative of excursion. Acceleration is the derivative of velocity and double derivative of displacement.
Lets say we have a driver with constant excursion versus frequency (such as a woofer well below resonance). We would see that it had a velocity that was rising 6dB per Octave as we go up in frequency. It would have an acceleration rising 12 dB per Octave with frequency.
Move to well above resonance and you are in a mass controlled region. For those frequencies acceleration is constant. When acceleration is constant for a range of frequencies then velocity wil be falling 6dB for every Octave we go up. Displacement will fall 12 dB per Octave. This is just the physics (or calculus) of oscillatory motion.
What do we want? We want flat SPL or flat radiated power (the same thing if directivity is constant) but to achieve that we have to look at the radiation impedance that the driver is working into. It turns out that a piston has a radiation that rises 12 dB per Octave for most of its working range. That means that constant displacement doesn't work, we need constant acceleration (12 dB falling excursion) to have flat response.
That is why a driver tends to give flat response above resonance and 12dB falling response below resonance.
David S.
But why would you continue to cling to that notion when there is no evidence to support it?
Linkwitz makes a throw-away statement while confusing kinetic energy in the driver with acceleration of the panels. He is speculating and gives no measurements or other corroboration.
I have given a link to the Harwood paper that shows no such fall off in cabinet resonant output with frequency. It shows that throughout the woofers range the cabinet resonances are about equally driven.
If that isn't enough pick up Martin Colloms' book High Performance Loudspeakers and read chapter 7 (in the 2nd edition). He has graphs by Barlow of a cabinet with 3 different wall thicknesses. Above the fundamental resonance it has flat output to 2k. He has graphs by Stevens showing the acoustical output of the rear panel of a cabinet with approx. equal resonant peaks to 2k. He has more curves by Barlow (I said Sowter the other day, sorry) comparing a damped and undamped 9mm thick cabinet. The undamped case shows strong energy up to 2k, the limits of the curve.
Plenty of curves are out there and none of them follow your 1 over f squared or 1 over f to the 4th roll off. Clearly in every measured case there is plenty of energy to excite their resonances across the frequency range (note that there is no threshold to exciting resonances. It is a linear effect, the curves would not change with drive level).
Show me a measurement that backs up your notion.
David S.
Slip of the pen, that should be excursion. Too bad diyaudio doesn't allow us to make corrections after a couple of minutes.
Speaker Dave I have read your replies and the article you listed and I have been thinking about it.
Last night I put some cross braces in the test cab I am building. Rapping on the sides confirmed that they had moved up in resonance - but I could also hear them ringing like a bell.
It convinced me that just as you say stiffness alone is not the answer. It is like a cymbal, which though VERY stiff, literally rings like a bell, just like my stiffened side panels are doing.
When a cymbal is struck it 'rings' for a very long time, unless some damping action occurs, such as putting a finger on it. Just the damping action of one finger can have a tremendous effect on the energy decay.
I am thinking perhaps I will build some kind of internal bracing that, instead of attaching directly, contacts the panels with something rubbery, like RTV perhaps - the 'finger' on the cymbal. This, in addition to conventional damping, should help considerably, judging from the information.
Last night I put some cross braces in the test cab I am building. Rapping on the sides confirmed that they had moved up in resonance - but I could also hear them ringing like a bell.
It convinced me that just as you say stiffness alone is not the answer. It is like a cymbal, which though VERY stiff, literally rings like a bell, just like my stiffened side panels are doing.
When a cymbal is struck it 'rings' for a very long time, unless some damping action occurs, such as putting a finger on it. Just the damping action of one finger can have a tremendous effect on the energy decay.
I am thinking perhaps I will build some kind of internal bracing that, instead of attaching directly, contacts the panels with something rubbery, like RTV perhaps - the 'finger' on the cymbal. This, in addition to conventional damping, should help considerably, judging from the information.
Some years back I tried to find "box sound radiation". It is easy enough to measure the enclosure panels acceleration, but this is a long ways from what actually gets radiated. In short, I was unable to find any box radiation of signifiicance, albeit my techniques were crude. The point is that it takes some very exacting measurements to even find this radiation. (These were of coarse my boxes, which are very rigid and well braced. I have no doubt that other boxes could be terrible.) I also attempted to find the sound radiation coming through the cone - couldn't find that either. I mean these things clearly exist but are they audibly significant? I have not found any evidence in my designs that they are. I have made uber rigid carbon fiber enclosure with contrained layer damping on all panels and compared those to far lessor constructions. Nothing measurable and nothing obviously audible.
There are so many other things to worry about.
There are so many other things to worry about.
Higher order modes, I presume?
The reason that Harwood wrote his paper was that they were able to (audibly) detect cabinet resonances at the BBC. Voice can be very revealing of resonances and we shouldn't discount the added discernment available when you can just walk into a studio, have a listen to some announcers or musicians, then walk back and sample the rendering by the monitor system.
One of the graphs in his paper (figure 12) shows the level and frequency points of all of the significant resonances of the systems that they sampled and differentiates between those they found audible and those that were not audible. Once the resonances had a radiation more that 30dB below the cone output they were good enough, but if they were above that level and above the middle hundreds in frequency, then the BBC researchers had no problem hearing them.
David S.
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